Phase-change materials (PCMs) are of broad interest for thermal storage and management applications. For energy-dense storage with fast thermal charging/discharging rates, a PCM should have a suitable melting temperature, large enthalpy of fusion, and high thermal conductivity. To simultaneously accomplish these traits, we custom design nanocomposites consisting of phase-change Bi nanoparticles embedded in an Ag matrix. We precisely control nanoparticle size, shape, and volume fraction in the composite by separating the nanoparticle synthesis and nanocomposite formation steps. We demonstrate a 50–100% thermal energy density improvement relative to common organic PCMs with equivalent volume fraction. We also tune the melting temperature from 236–252 °C by varying nanoparticle diameter from 8.1–14.9 nm. Importantly, the silver matrix successfully prevents nanoparticle coalescence, and no melting changes are observed during 100 melt–freeze cycles. The nanocomposite’s Ag matrix also leads to very high thermal conductivities. For example, the thermal conductivity of a composite with a 10% volume fraction of 13 nm Bi nanoparticles is 128 ± 23 W/m-K, which is several orders of magnitude higher than typical thermal storage materials. We complement these measurements with calculations using a modified effective medium approximation for nanoscale thermal transport. These calculations predict that the thermal conductivity of composites with 13 nm Bi nanoparticles varies from 142 to 47 W/m-K as the nanoparticle volume fraction changes from 10 to 35%. Larger nanoparticle diameters and/or smaller nanoparticle volume fractions lead to larger thermal conductivities.